PGA: A new particle swarm optimization algorithm based on genetic operators for the global optimization of clusters

We have developed a global optimization program named PGA based on particle swarm optimization algorithm coupled with genetic operators for the structures of atomic clusters. The effectiveness and efficiency of the PGA program can be demonstrated by efficiently obtaining the tetrahedral Au₂₀ and double-ring tubular B₂₀, and identifying the ground state ${\text{ZrSi}}_{17–20}^{-}$ clusters through the comparison between the simulated and the experimental photoelectron spectra (PESs). Then, the PGA was applied to search for the global minimum structures of ${\mathrm{Mg}}_n^{-}$ (n = 3–30) clusters, new structures have been found for sizes n = 6, 7, 12, 14, and medium-sized 21–30 were first determined. The high consistency between the simulated spectra and the experimental ones once again demonstrates the efficiency of the PGA program. Based on the ground-state structures of these ${\mathrm{Mg}}_n^{-}$ (n = 3–30) clusters, their structural evolution and electronic properties were subsequently explored. The performance on Au₂₀, B₂₀, ${\text{ZrSi}}_{17–20}^{-}$, and ${\mathrm{Mg}}_n^{-}$ (n = 3–30) clusters indicates the promising potential of the PGA program for exploring the global minima of other clusters. The code is available for free upon request.